Computer Science > Symbolic Computation
[Submitted on 9 Jun 2023 (v1), last revised 3 Nov 2023 (this version, v2)]
Title:Positivity certificates for linear recurrences
View PDFAbstract:We consider linear recurrences with polynomial coefficients of Poincaré type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a precisely defined genericity condition. For positive sequences, the algorithm produces a certificate of positivity that is a data-structure for a proof by induction. This induction works by showing that an explicitly computed cone is contracted by the iteration of the recurrence.
Submission history
From: Bruno Salvy [view email][v1] Fri, 9 Jun 2023 14:44:38 UTC (28 KB)
[v2] Fri, 3 Nov 2023 12:58:56 UTC (53 KB)
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